401-3660-69L  Numerical Analysis Seminar: Model Order Reduction and Reduced Bases for PDEs

SemesterHerbstsemester 2019
DozierendeC. Marcati
Periodizitäteinmalige Veranstaltung
LehrspracheEnglisch
KommentarNumber of participants limited to 5. Consent of Instructor needed.



Lehrveranstaltungen

NummerTitelUmfangDozierende
401-3660-69 SNumerical Analysis Seminar: Model Order Reduction and Reduced Bases for PDEs
Bewilligung der Dozierenden für alle Studierenden notwendig.
Instructor: Dr. Carlo Marcati
2 Std.
01.10.12:15-13:00HG D 3.1 »
30.10.09:15-12:00HG F 26.3 »
18.12.13:15-18:00HG F 26.1 »
21.01.09:15-12:00HG G 26.3 »
C. Marcati

Katalogdaten

KurzbeschreibungReduced Basis (RB) methods provide a technique to reduce the computational cost of problems described by partial differential equations which involve a wide range of parameters (parametric PDEs). Such problems are ubiquitous in science and engineering, both in the analysis of physical phenomena and in the design of new objects.
LernzielThe aim of this seminar is to review recent mathematical results on theoretical aspects of Reduced Basis
methods and to learn how model-order reduction techniques can be used to lower
computational cost in the solution of parametric PDEs.
InhaltReduced Basis (RB) methods provide a technique to reduce the computational cost of
problems described by partial differential equations which involve a wide range
of parameters (parametric PDEs). Such problems are ubiquitous
in science and engineering, both in the analysis of physical phenomena and in
the design of new objects.

Building on top of classical
finite element approximations, RB methods split the work into a
computationally heavy offline phase and an online phase—where
only a reduced-order model needs to be solved—that can be executed almost in real-time.
The first phase involves computing the high-fidelity solutions to the PDE on a carefully
selected "training" set of parameters (so-called snapshots). The snapshots are then
used as a reduced basis (hence the name of the method) for the solution of problems on new parameters.
The methods used for the (quasi-)optimal selection of the basis are of independent interest
and shared with other model-order reduction techniques in statistics, approximation, and
data science.

The estimates on a priori RB errors are linked with the
approximability of the classes of solutions to the equations; furthermire, reduced approximations can be used as a theoretical tool
in the analysis of other reduction techniques.
LiteraturIntroductory textbooks.

[1] Jan S. Hesthaven, Gianluigi Rozza, and Benjamin Stamm, Certified reduced basis
methods for parametrized partial differential equations, SpringerBriefs in Mathemat-
ics, Springer, Cham; BCAM Basque Center for Applied Mathematics, Bilbao,
2016.

[2] Alfio Quarteroni, Andrea Manzoni, and Federico Negri, Reduced basis methods
for partial differential equations, Unitext, vol. 92, Springer, Cham, 2016.
Voraussetzungen / BesonderesFormat of the seminar
The seminar format will be oral student presentations, combined with a written report.
Student presentations will be
based on a recent research paper selected in two meetings
at the start of the semester.

Leistungskontrolle

Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs
ECTS Kreditpunkte4 KP
PrüfendeC. Marcati
Formunbenotete Semesterleistung
PrüfungsspracheEnglisch
RepetitionRepetition nur nach erneuter Belegung der Lerneinheit möglich.
ZulassungsbedingungCompleted BSc MATH ETH and Consent of Instructor
Zusatzinformation zum PrüfungsmodusPassing grade will require
a) 1hr oral presentation with Q/A from the seminar group and
b) typed seminar report (``Ausarbeitung'') of several key aspects of the paper under review.

Lernmaterialien

 
HauptlinkInformation
Es werden nur die öffentlichen Lernmaterialien aufgeführt.

Gruppen

Keine Informationen zu Gruppen vorhanden.

Einschränkungen

AllgemeinBewilligung der Dozierenden für alle Studierenden notwendig
PlätzeMaximal 5
BelegungsbeginnBelegung ab 08.08.2019 möglich
VorrangDie Belegung der Lerneinheit ist nur durch die primäre Zielgruppe möglich
Primäre ZielgruppeMathematik MSc (437000)
Angewandte Mathematik MSc (437100)
WartelisteBis 19.09.2019

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StudiengangBereichTyp
Mathematik MasterSeminareWInformation